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In this paper, we adopt the variance premium principle to investigate the problem of optimal dividends and reinsurance in a diffusion approximation risk model with thinning-dependence structure. We first study the optimal problem without capital injection. We then consider the incorporation of forced capital injection into the model whenever the reserve level drops below zero. We finally turn to the general problem in which capital injection is allowed but not compulsory. For the three optimal problems, we apply the technique of stochastic control theory to obtain closed-form expressions for the optimal strategies and the corresponding value functions for two classes of insurance business with thinning dependence. Under the assumption of non cheap reinsurance, we obtain results that are quite different from those in the case of cheap reinsurance for both bounded and unbounded dividend rates. Furthermore some numerical examples are presented to show the effect of parameter values on the optimal policies. [ABSTRACT FROM AUTHOR]

In this paper, we consider an optimal robust reinsurance problem in a diffusion model for an ambiguity-averse insurer, who worries about ambiguity and aims to minimize the robust value involving the probability of absolute ruin and a penalization of model ambiguity. It is assumed that the insurer is allowed to purchase per-claim reinsurance to transfer its risk exposure, and that the reinsurance premium is computed according to the mean-variance premium principle which is a combination of the expected-value and variance premium principles. The optimal reinsurance strategy and the associated value function are derived explicitly by applying stochastic dynamic programming and by solving the corresponding boundary-value problem. We prove that there exists a unique point of inflection which relies on the penalty parameter greatly such that the robust value function is strictly concave up to the unique point of inflection and is strictly convex afterwards. It is also interesting to observe that the expression of the optimal robust reinsurance strategy is independent of the penalty parameter and coincides with the one in the benchmark case without ambiguity. Finally, some numerical examples are presented to illustrate the effect of ambiguity aversion on our optimal results. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the problem of optimal reinsurance and dividends under the Cramér–Lundberg risk model with the thinning-dependence structure which was first introduced by Wang and Yuen [Wang, G. & Yuen, K. C. (2005). On a correlated aggregate claims model with thinning-dependence structure. Insurance: Mathematics and Economics 36(3), 456–468]. The optimization criterion is to maximize the expected accumulated discounted dividends paid until ruin. To enhance the practical relevance of the optimal dividend and reinsurance problem, non-cheap reinsurance is considered and transaction costs and taxes are imposed on dividends. These realistic features convert our optimization problem into a mixed classical-impulse control problem. For the sake of mathematical tractability, we replace the Cramér–Lundberg risk model by its diffusion approximation. Using the method of quasi-variational inequalities, we show that the optimal reinsurance follows a two-dimensional excess-of-loss reinsurance strategy, and the optimal dividend strategy turns out to be an impulse dividend strategy with an upper and a lower barrier, i.e. everything above the lower barrier is paid as dividends whenever the surplus goes beyond the upper barrier, and no dividends are paid otherwise. Under the diffusion risk model, closed-form expressions for the value function associated with the optimal dividend and reinsurance strategy are derived. In addition, some numerical examples are presented to illustrate the optimality results. [ABSTRACT FROM AUTHOR]

This paper studies the optimal investment and reinsurance problem for a risk model with premium control. It is assumed that the insurance safety loading and the time-varying claim arrival rate are connected through a monotone decreasing function, and that the insurance and reinsurance safety loadings have a linear relationship. Applying stochastic control theory, we are able to derive the optimal strategy that maximizes the expected exponential utility of terminal wealth. We also provide a few numerical examples to illustrate the impact of the model parameters on the optimal strategy. [ABSTRACT FROM AUTHOR]

This paper considers an optimal asset-liability management (ALM) problem for an insurer under the mean-variance criterion. It is assumed that the value of liabilities is described by a geometric Brownian motion (GBM). The insurer's surplus process is modeled by a general jump process generated by a marked point process. The financial market consists of one risk-free asset and n risky assets with the risk premium relying on an affine diffusion factor process. By transferring a proportion of insurance risk to a reinsurer and investing the surplus into the financial market, the insurer aims to maximize the expected terminal net wealth and, at the same time, minimize the corresponding variance of the terminal net wealth. By using a backward stochastic differential equation (BSDE) approach, closed-form expressions for both the efficient strategy and efficient frontier are derived. To illustrate the main results, we study an example with the Heston stochastic volatility (SV) model and numerically analyze the economic behavior of the efficient frontier. Finally, a generalization of the Mutual Fund Theorem is obtained. [ABSTRACT FROM AUTHOR]

In this paper, we consider the problem of optimal investment-reinsurance with two dependent classes of insurance risks in a regime-switching financial market. In our model, the two claim-number processes are correlated through a common shock component, and the market mode is classified into a finite number of regimes. We also assume that the insurer can purchase proportional reinsurance and invest its surplus in a financial market, and that the values of the model parameters depend on the market mode. Using the techniques of stochastic linear-quadratic control, under the mean–variance criterion, we obtain analytic expressions for the optimal investment and reinsurance strategies, and derive closed-form expressions for the efficient strategies and the efficient frontiers which are based on the solutions to some systems of linear ordinary differential equations. Finally, we carry out a numerical study for illustration purpose. [ABSTRACT FROM AUTHOR]

In this paper, we consider the optimal proportional reinsurance problem in a risk model with the thinning-dependence structure, and the criterion is to minimize the probability that the value of the surplus process drops below some fixed proportion of its maximum value to date which is known as the probability of drawdown. The thinning dependence assumes that stochastic sources related to claim occurrence are classified into different groups, and that each group may cause a claim in each insurance class with a certain probability. By the technique of stochastic control theory and the corresponding Hamilton-Jacobi-Bellman equation, the optimal reinsurance strategy and the corresponding minimum probability of drawdown are derived not only for the expected value principle but also for the variance premium principle. Finally, some numerical examples are presented to show the impact of model parameters on the optimal results. [ABSTRACT FROM AUTHOR]

In this paper, we consider the optimal proportional reinsurance strategy in a risk model with two dependent classes of insurance business, where the two claim number processes are correlated through a common shock component. Under the criterion of maximizing the expected exponential utility with the variance premium principle, we adopt a nonstandard approach to examining the existence and uniqueness of the optimal reinsurance strategy. Using the technique of stochastic control theory, closed-form expressions for the optimal strategy and the value function are derived for the compound Poisson risk model as well as for the Brownian motion risk model. From the numerical examples, we see that the optimal results for the compound Poisson risk model are very different from those for the diffusion model. The former depends not only on the safety loading, time, and the interest rate, but also on the claim size distributions and the claim number processes, while the latter depends only on the safety loading, time, and the interest rate. [ABSTRACT FROM PUBLISHER]

In this paper, we consider the jump-diffusion risk model with proportional reinsurance and stock price process following the constant elasticity of variance model. Compared with the geometric Brownian motion model, the advantage of the constant elasticity of variance model is that the volatility has correlation with the risky asset price, and thus, it can explain the empirical bias exhibited by the Black and Scholes model, such as volatility smile. Here, we study the optimal investment-reinsurance problem of maximizing the expected exponential utility of terminal wealth. By using techniques of stochastic control theory, we are able to derive the explicit expressions for the optimal strategy and value function. Numerical examples are presented to show the impact of model parameters on the optimal strategies. Copyright © 2011 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper studies the optimal reinsurance and investment strategy for an insurer with two dependent classes of insurance business, where the claim number processes are correlated through a common shock. It is assumed that the insurer also faces the decision making of investing in a financial market with one risk-free asset and one risky asset following the Heston stochastic volatility (SV) model. The insurer is not allowed to short sell the risky asset. Under the mean–variance criterion, we consider the insurer's problem of maximizing the expected terminal wealth and, at the same time, minimizing the variance of the terminal wealth. Using the results of stochastic linear–quadratic (LQ) optimal control and backward stochastic differential equations (BSDEs), we derive closed-form expressions for the optimal strategies and the efficient frontiers in terms of solutions to the BSDEs. Our approach shows how BSDEs can be used to solve mean–variance problems in insurance applications. Finally, economic behavior of the efficient frontiers is analyzed by using some numerical examples. [ABSTRACT FROM AUTHOR]